Does the use of leverage impact the idiosyncratic risk-return relationship of listed REITs in the Netherlands, Belgium and France?

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University of Amsterdam, Amsterdam Business School

Master in Real Estate Finance

Does the use of leverage impact the idiosyncratic

risk-return relationship of listed REITs in the

Netherlands, Belgium and France?

July 2015

By

Caroline Beijdorff (0477680)

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Statement of originality:

This document is written by Student Caroline Beijdorff who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

This thesis examines whether the use of leverage impacts the relationship between returns and idiosyncratic risk for listed REITs. This thesis shows that – contrary to the CAPM theory- significant negative relationship is found between idiosyncratic risk and returns for Belgian, Dutch and French listed REITs during the crisis, and that this relationship is significantly positive for the post-crises period. This finding suggests that idiosyncratic risk does indeed matter for REIT pricing. This thesis also studies the role third party debt plays in the

idiosyncratic risk-return relationship. During the crisis there is a significant negative relationship between leverage and returns but even though leverage seems to be associated with higher idiosyncratic risk it does not seem to play a significant role in the idiosyncratic risk return relationship.

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1. Introduction

Both modern portfolio theory (MPT) and its extension the capital asset pricing model (CAPM) (both discussed later in this thesis) suggest that all investors should hold a theoretical market portfolio and that the idiosyncratic or firm specific risk of an individual stock is diversified away. As such the only risk that is priced into investment returns is systematic risk. The pricing of idiosyncratic risk is left out of the equation.

In practice no investor can hold the (theoretical) market portfolio. Most investors even cannot hold the approximation of the (theoretical) market portfolio and therefore cannot completely eliminate idiosyncratic risk through diversification. For example, from the perspective of smaller institutional or individual investors or a portfolio manager specialised in real estate, who –for practical purposes- are unable to hold a large portfolio of diversified stocks, idiosyncratic risk is important. Merton (1987) hypothesises that when investors are unable to invest in the market portfolio they will be concerned with total risk. Goetzmann and Kunmar (2008) find that in reality a significant amount of individual investors hold under-diversified portfolios. Furthermore they show that“investors who over-weight stocks with higher volatility and higher

skewness are less diversified”. If so, then investors may expect additional return for holding the associated idiosyncratic risk. As we will see there is conflicting evidence whether idiosyncratic is indeed priced in or not.

Also in the case of a manager of a firm holding stock options of that firm, this manager will be interested in idiosyncratic risk, as his/her stock options are per definition undiversified. This is also true for the broader case of the pricing of options generally or in the case of arbitrage. In these cases both components of risk (market and idiosyncratic) are relevant.

Regulation and legislation also prevent investors from freely holding the market portfolio. In response to the recent financial crisis new rules and regulation have been implemented for investment management such as MIFID and gradually since 2013 the Alternative Investment Manager Directive. The appropriate

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management of risks by the fund manager is one of the central themes of the new AIFMD regulation (regulation to be found at http://eur-lex.europa.eu/legal-content). The applicability of this law is to all alternative investment funds, i.e. Real Estate Funds, Private Equity Funds and Hedge Funds with total assets under management of EUR 500 mln unlevered assets or -if levered-total assets under management of EUR 100 mln. For funds with EUR 100-500 mln assets under management, the use of even 1 EURO of leverage is therefore an important determinant on whether this complex legislation is applicable or not. Throughout the AIFMD legislation (as can be read online at http://eur-lex.europa.eu/legal-content), leverage is assumed to be an important

determinant of the overall riskiness of alternative investment funds. The effect leverage has on the general riskiness of a fund is therefore also increasingly relevant to fund managers of alternative funds from a more broader perspective, as fund managers are finding that risk management is increasingly one of central themes of their daily business.

With respect to the evidence of pricing of idiosyncratic risk –as suggested by Merton (1987)- a number of papers have been published with respect to idiosyncratic risk-return relationship of (US) REITs)(such as Ooi et al. (2009), Sun and Yung (2009) and DeLisle et al. (2013), all discussed in the next section). All three papers correct for firm specific factors such as firm size,

book-to-market equity, momentum, liquidity costs , transaction costs and institutional ownership. None of the aforementioned papers correct for the effects of

leverage, even though Chaudry et al. (2004) find that for the period after 2000 the relationship between leverage and idiosyncratic risk is significant for US listed REITs.

In a deterministic manner leverage does affect returns as it amplifies returns to shareholders, either in a positive or a negative sense. As shown by Hamada (1972) -when CAPM and the Modigliani-Miller (MM) Theorem (1958) are combined- leverage affects a firm’s beta in a linear manner. This linear

relationship is however dependent on the beta of the third party debt being zero. This zero beta assumption is realistic in settings of low to moderate leverage.

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Real Estate Investment Trusts (REITs) however are traditionally dependent on high levels of debt for the funding of their activities.

To recapitulate: if -on the one hand- a significant number of investors cannot hold the market portfolio they may expect additional return for holding idiosyncratic risk. This thesis investigates whether investors indeed receive a return for idiosyncratic risk for Dutch, Belgian and French listed REITs. And if – on the other hand- the assumptions underlying the MM Theorem and the derived Hamada equation that describe the linear relationship between leverage and beta do not hold for REITs in the real world, investors should –according to Merton (1987)- again demand an additional return, in this case for leverage. This thesis also investigates whether investors indeed do receive additional return for leverage, whether this potential pricing is directly or through the pricing of idiosyncratic risk. In effect this thesis analyses whether leverage has an impact on the idiosyncratic risk-return relationship.

This study uses a different data set (i.e. European listed REITs) than all previous REIT idiosyncratic risk studies (i.e.US listed REITs). Moreover the data set is over a different time period (i.e.2004-2014) than most studies. Only DeLisle et al. (2013) covers the crisis period (i.e. 2007-2009) and even their study does not cover the post-crisis period (i.e. after 2010). Moreover this thesis is the only study so far on the impact of leverage on the risk-idiosyncratic return relationship for listed REITs.

This thesis shows that –contrary to the CAPM theory- significant negative relationship is found between idiosyncratic risk and returns for Belgian, Dutch and French listed REITs during the crisis, and that this relationship is

significantly positive for the post-crises period. This finding suggests that idiosyncratic risk does indeed matter for REIT pricing. This thesis also studies the role third party debt plays in the idiosyncratic risk-return relationship. During the crisis there is a significant negative relationship between leverage and returns but even though leverage seems to be associated with higher idiosyncratic risk it does not seem to play a significant role in the idiosyncratic risk return relationship.

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The remaining part of this thesis is structured as follows: chapter 2 provides background in the form of a literature review and some high level information on European REITs. Chapter three describes the data used and the research

methodology, chapter four discusses the results and finally chapter five provides a conclusion.

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2. Literature review and background

2.1 Literature review

Pricing of risk in an investment portfolio

Modern portfolio theory or mean-variance portfolio theory (MPT) is centred on the assumption that diversification reduces the riskiness of expected returns. In other words it is based on the “don’t put all of your eggs in one basket” principle. When returns of individual assets are less than perfectly correlated with each other, a portfolio holding these assets will always offer a better risk-return profile than the individual assets on their own.

Markowitz (1952) showed that under a set of assumptions the variance of the expected return is a meaningful measure of risk. The formula for portfolio variance he derives shows both the importance of diversification and how to do it, i.e. how much to hold of each asset. In essence Markowitz is saying that the prospects for any asset can be described by just three variables: the reward (i.e. expected return) and the risk (i.e. expected volatility of returns) and the

covariance (expected co-movement between individual returns) with other assets within the portfolio.

The expected return of a portfolio is calculated as the capital weighted average returns on each asset in the portfolio. The key however to portfolio approach is that when two (or more) random variables are not perfectly correlated, the variance of these variables is less than the sum of their variance. The variance of a portfolio encompasses not only the weighted average of the individual asset variances but also includes the weighted covariances between pairs of individual assets. This means you can lower your risk by merely holding more than one asset. As the number of assets grows the portfolio variance goes to a (low) constant level. This means that covariance is what counts in a large portfolio. This covariance is the part of risk, which can be attributed to common factors, and this is known as systematic risk or market risk. Since systematic or market

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risk cannot be diversified away, diversification addresses the eliminations of unsystematic or idiosyncratic risk. This is the risk that cannot be attributed to common factors.

In a practical sense diversification in real estate portfolios is a task made difficult by the very nature of real estate. Large lot sizes, high transaction costs and the non-divisibility make that the construction of a very large portfolio of individual assets is -for some investors at least - impractical. Brown and Matysiak (2001) show that low correlations between individual properties returns can lead to a portfolio risk reductions between 62% and 70% for a portfolio of 30 properties. However they also show that each property and portfolio also show a large portion of idiosyncratic risk which cannot be diversified away. This means that portfolio returns are very much influenced by the characteristics of individual properties rather than the market factor. Brown and Matysiak (2001) conclude that “although it is possible to achieve significant reductions in risk it is very difficult to achieve high levels of diversification”. Callender et al. (2007) showed that “a large measure of risk reduction can be achieved with portfolios of 30-50 properties, but full diversification of idiosyncratic risk can be achieved only in very large portfolios” i.e. 200 and more properties.

In what is known as the separation theorem Sharpe (1963) and others showed that regardless of risk preferences every investor will want hold the same optimal portfolio of risky assets just in different (relative) amounts. They showed that the calculation of the optimal portfolio is done in two steps: first to find the optimal risky portfolio on the efficient frontier, i.e. the market portfolio. This optimal risky market portfolio is held to encompass all assets in the

investment universe.

Secondly they realised that one could construct a portfolio outside the efficient portfolio set by the introduction of a risk free rate in combination to the market portfolio on the efficient frontier. By altering the proportion of funds invested in the risk free asset and the optimal market portfolio it is possible to construct a portfolio to satisfy ones risk appetite. This model as described above has come to be known as the Capital Asset Pricing Model or CAPM.

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As discussed, systematic risk arises from the general variability of asset prices. According CAPM it is only this portion - the systematic component of the variability in returns - which in theory is priced in the market place. The risk premium of the market portfolio is its expected return minus the risk free rate ((𝑅𝑚− 𝑅𝑓). As the general market moves, the extent to which an individual

assets co-moves with this market is expressed by 𝛽𝑖. Or:

𝐸(𝑅_𝑖) = 𝑅_𝑓+ 𝛽_𝑖(𝑅_𝑚− 𝑅_𝑓) + 𝜀_𝑖 (1)

In other words in theory it is only the covariance with the market return that is relevant to an investor and it is therefore the only risk, which is priced.

According to theory the residuals 𝜀_𝑖, or idiosyncratic risk would not be priced. There have been through the years many extensions to the CAPM model, and one of them is the Fama-French (1993) three-factor model. This model introduces two extra factors into the risk-return equation, firm size and equity book-to-market ratio. They observed that small caps and stocks with a low price-to-book ratio tended to outperform the rest of the market. This is the model that is used in most of the research which is discussed next. The other model also used in this thesis is the Carhart (1997) four factor model which adds a momentum factor to the Fama-French factors.

Merton (1987) hypothesises that small investors who are unable to hold the (hypothetical) market portfolio and who do not have full access to information, may have a preference for stocks they are familiar with. In this case, total risk and more specifically idiosyncratic risk is what these investors will be concerned with.

Research linking idiosyncratic risk to returns show mixed results and seem to be dependent on the chosen time frame and the manner in which idiosyncratic risk is measured and the number and type of factors controlled for.

For instance Ang et al. (2006) show that US monthly stock returns are negatively related to one month lagged idiosyncratic risk. However these findings can possibly be explained by a subset of small stocks with high idiosyncratic

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volatilities. Ang et al. (2009) extend the study across 23 developed markets and still find “that there is a strong covariation in low returns to high-idiosyncratic-volatility stocks across countries even when controlling for world market, size and value factors”.

Fu (2009) focuses on the time varying aspects of idiosyncratic volatility and uses exponential generalised autoregressive conditional heteroscedasticity

(EGARCH)models to estimate expected idiosyncratic risk. He finds a positive relationship between expected returns and the estimated conditional

idiosyncratic volatilities. However Guo et al. (2014) show that the method used by Fu (2009) introduces a look ahead bias, and that when is corrected for the positive relationship between expected returns and idiosyncratic risk

disappears.

Fink et al. (2010) find that the age characteristics of the firm drives the

idiosyncratic risk of listed firms, and when they control for the age of a firm they find no abnormal spike in idiosyncratic risk during the internet boom.

Recently a number of papers have been written specifically describing REIT idiosyncratic risk. One example is Ooi et al. (2009). Using US REIT data over the period 1990-2005 they use EGARCH to model a time varying idiosyncratic risk. They find a positive relationship between the idiosyncratic risk of US REITs and a cross-section of US REIT returns. Moreover they also find that 78% of the total REIT return volatility is idiosyncratic in nature thus dominating market risk. However -as previously mentioned- according to Guo et al. (2013) this EGARCH estimation method of estimating idiosyncratic risk introduces a look-ahead bias., which if controlled for could render this positive relationship insignificant. Sun and Yung (2009) do not use EGARCH in their firm level study and initially also find a positive relationship between idiosyncratic risk and expected returns. Once they eliminated certain REITs out of the sample -i.e. small, low priced illiquid stocks- this positive relationship becomes insignificant.

Chiang et al. (2009) also study the time-series relationship between idiosyncratic risk and REIT returns and find a positive relationship before 1992 and a negative

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relationship in the time period 1992-2006. They perform their analysis on a portfolio level without using EGARCH.

The Ooi et al. (2009) finding that total return volatility is dominated by

idiosyncratic risk is confirmed by DeLisle et al. (2013). However they also show that -consistent with the non-REIT study of Ang et al. (2006, 2009)- idiosyncratic risk is negatively priced, and that systematic risk is not priced in US REIT returns (1996-2010). They do this by avoiding the limitations in market beta by using a number of different implied market volatility measures. This analysis is

performed both at firm level and at portfolio level. The results remain significant after controlling for a number of firm specifics such as, idiosyncratic skewness, firm size, book-to-market equity, momentum, institutional ownership and liquidity. This is in contrast with the findings of Ooi et al. (2009) REIT study. Chaudry et al. (2004) performed an analysis on the relationship between idiosyncratic risk and several REIT characteristics such as, size, operating performance, leverage, liquidity and earnings variability. They did however not examine the (idiosyncratic) risk return relationship in combination with these firm specific characteristics.

None of the above mentioned REIT studies capture the potential effects of the capital structure in the analysis even though –due to their activities- a relatively high LTV ratio is quite normal for REITs. Especially in situations where credit conditions are tight this industry wide high leverage could potentially impact the risk-return relationship.

Capital structure of a firm

The famous Modigliani-Miller (MM) Theorem (1958) forms a theoretical basis for the modern approach to a company’s financing mix and capital structure. The MM proposition I states that -in a perfect capital market- a firm’s capital

structure is irrelevant to its total value. In this perfect capital market, the value of a firm is determined by its real assets (i.e. left-hand side of the balance sheet) rather than its financing mix (i.e. right-hand of the balance sheet). An implicit assumption to this theorem is that both the (real estate) company and the

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investor can lend and borrow at the same (risk-free) rate. As such investors can offset any effects of shifts in capital structure, i.e. when the (real estate) company lends the investor can borrow and vice versa.

MM proposition II states that an investor’s expected rate of return should

increase as the company applies more leverage. Financing assets with borrowed capital makes sense when the expectation is that the profits made will be greater than the net interest payable, i.e. the net interest rate is lower than the expected return of the property. The use of financial leverage however will magnify the variability in earnings available to investors. So any increase in and investor’s expected return is offset by an increase in the company’s (financial) risk and therefore the investor’s required return. So as leverage increases the total risk (of the asset) is the same, while the burden of individual risks is shifted from one investor class to another. Also as a company borrows more, financing costs will increase (in a non-linear manner) as the result of potential financial distress (such as bankruptcy costs, i.e. auditors fees, legal fees, reduced management attention to operations etc.). Also as leverage increases the debt holder will require a higher rate of return, i.e. the company’s interest rates will rise. This causes the rate of increase of the investor’s required return to decrease.

The MM theorem as a whole provides a base with which to examine reasons why capital structure is in fact relevant. This is because existing capital markets are in fact far from perfect and in the real world a company's value is in fact affected by its financing choices. Some of these market imperfections include transaction costs, taxes, costs of financial distress, agency costs, and information asymmetry. However Gomes & Schmid (2010) relax a number of MM’s assumptions but still find a positive relationship between leverage and (risk adjusted) expected returns when they control for firm size and book-to-market value.

Faulkender & Peterson (2005) investigate whether the source of capital

(banking vs. capital markets) impact the capital structure of firms. They find that controlling for other factors having access to the bond market results in having more leverage. Grovenstein et al. (2005) investigate how well commercial mortgage underwriters manage their risks and find that low Loan-to-Value

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(LTV’s) loans appear to have higher than average risks, something lenders compensate for in the loan pricing.

Westgaard et al. (2008) investigate determinants of the capital structure of non-listed UK real estate companies (1998-2006) and find inter alia a positive relationship between profitability, tangibility and size on the one hand and leverage on the other hand. They also find that the correlation between leverage -on the one hand- and asset turnover and earnings variability –on the other hand- is negative.

Van der Spek & Hoorenman (2011) investigate European non-listed (INREV) funds and find that portfolio’s with a leverage up to 40% are still efficient but that for higher LTV’s the costs of financial distress, asymmetric performance fees and the impact of higher interest rates make further leverage inefficient. Fuerst & Matysiak (2013) also investigate the performance of European non-listed real estate funds (2001-2007) and the relationship with – amongst other factors- leverage. They find that higher LTV’s lead to higher returns but in their conclusion they point out that the contribution of increased riskiness in the increased return has not been included in this study. According to theory an increase in LTV should lead to a higher return but this is associated with a higher risk.

Giacomini et al. (2014) investigate the relationship between leverage and real estate returns using publically traded REIT data (2002-2011) from eight different countries. They find that leverage has an effect on realised returns. They also find that the greater use of leverage during the 2007-2008 crisis was associated with larger than average price declines.

Finally Sun et al. (2015) also link the leverage ratio to commercial real estate return’s using US REIT data (2006-2011) and focus on the crisis years. They find that REITs with higher LTV ratios and shorter maturity profiles (used as a proxy for the costs of financial distress) show larger price declines than REITs with lower LTV ratios and longer maturity profiles.

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Combining capital structure with CAPM

If CAPM and the MM theorem are combined one can derive that leverage increases the beta of a firm. Derived equations that show the relationship between leverage and beta is proposed by Hamada (1972). Hamada’s equation (1972) relates the beta of a levered firm to that of an unlevered firm and shows that leverage increases the CAPM beta in a linear way:

𝛽𝐿 = 𝛽𝑈[1 + (1 − 𝑇) ∗ 𝐷/𝐸] (2)

where β_L and β_U are the levered and unlevered Betas respectively, T is the tax rate and D/E is the debt equity ratio (or leverage ratio). In the case of REITs the tax rate is effectively zero and the levered beta is equal to the unlevered beta plus the unlevered beta times the leverage. Thus according to Hamada(1972) leverage affects systemic risk in a linear manner.

The linear amplification effects of leverage on beta are in effect described in Giacomini et al (2014) where they show that unlevered mean returns are lower and significantly less volatile than levered returns. This finding is in concordance with the Hamada equation above. The volatility they describe however is total return volatility rather than a formal partitioning into systemic and

idiosyncratic volatility. Implicitly the assumption is made that leverage only affects beta.

One of the assumptions underlying the Hamada (1972) as described above is that the beta of third party debt equals zero. In practice this is likely to be the case for low to moderate leverage. In cases of high leverage or in case of tight credit conditions however the potential costs of financial distress become more important. These costs, such as potential bankruptcy costs (i.e. auditors fees, legal fees, reduced management attention to operations etc.), could very well result in the beta of third party debt to be larger than zero. In effect the linear relationship between CAPM beta and leverage then breaks down. Possibly the effects of leverage could then spill over into idiosyncratic risk. If this were the case then taking leverage into account could explain the non-zero

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Real Estate Investment Trusts (REITs) are traditionally dependent on high levels of debt for the funding of their activities. In the first place this is because they can, i.e. the relatively high tangibility of their balance sheets enable them to borrow relatively large amounts. This is because real estate is seen as attractive collateral by banks. In addition to this REITs also borrow relatively more

because they must. As discussed in the next section REITs enjoy a privileged tax status in return for a number of restrictions, one of these restrictions being the obligation to pay-out 80% or more (depending on jurisdiction) of net income. This leaves REITs relatively dependent on external financing, leading to relatively high LTVs when compared to other industries. This relatively high usage of third party debt could lead to the zero debt beta assumption to break down for REITs.

To recapitulate: if -on the one hand- a significant number of investors cannot hold the market portfolio they may expect additional return for holding idiosyncratic risk. This thesis investigates whether investors indeed receive a return for idiosyncratic risk for Dutch, Belgian and French listed REITs. And if – on the other hand- the assumptions underlying the MM Theorem and the derived Hamada equation that describe the linear relationship between leverage and beta do not hold for REITs in the real world, investors should –according to Merton (1987)- again demand an additional return, in this case for leverage. This thesis also investigates whether investors indeed do receive additional return for leverage, whether this potential pricing is directly or through the pricing of idiosyncratic risk. In effect this thesis analyses whether leverage has an impact on the idiosyncratic risk-return relationship.

2.2 Overview of European REIT regimes

REIT structures across the world offer real estate related firms to avoid taxation at entity level in exchange for a number of restrictions in -amongst other things- dividend pay-out ratios, share ownership, capital structure and the type of activity a REIT can engage in. The US has the oldest REIT regime in the world that was created in 1960. The Dutch followed in 1969 with the Fiscale Beleggings Instelling (FBI). Belgium passed REIT legislation in 1995, while France

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introduced the Societe d’Investissement Immobilier Cotee (SIIC) in 2003.

Germany introduced its own version of the REIT regime in 2007. There are quite a number of variations in the European REIT regimes the most important of which are described below.

Most countries restrict dividend pay-out ratios. For instance in the Netherlands the minimum dividend pay-out ratio has been set at 80% of taxable income payable within 8 months after the end of fiscal year. In Belgium –just as in the Netherlands- 80% of the net profit must be distributed. In France 85% of net rental income plus 100% of dividends from subsidiaries must be paid out as dividends.

In the Netherlands the restriction with respect to shareholder are quite

complicated with a different set of rules for regulated and non-regulated REITs. In practice all listed REITs are regulated. An individual (entity) may not hold more than 25%(45%) of the outstanding stock, and 75% or more of stock must be held by either individuals, regulated or non-tax paying entities. In Belgium there are no restrictions with respect to the shareholders. In France however no one shareholder may hold more than 60% in a SICC plus at least 15% of the shares at the beginning of the fiscal year must be owned by shareholders who do not have more than 2% of the voting rights.

With respect to financing restrictions: in the Netherlands debt may not exceed more than 60% of the tax book value of the real estate investments plus 20% of the fiscal book value of other investments. In Belgium debt may not exceed more than 65% plus the interest expense may not exceed 80% of the net income. France has no formal restrictions to the use of leverage for REITs but there are some practical limitations as in France REITs are per definition listed.

In the Netherlands the activity must be limited to investment management activities, though real estate (re)development activities are tolerated (with limitations) for the own portfolio. In Belgium the main activity must be passive investment in real estate. No more than 20% of total assets may be invested in a single property. Development activities are allowed for the own portfolio. In

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France the principle activity must be passive real estate investing but any other activities (such as ((re)development) are permitted up to 20% of the total assets. To recapitulate, REITs are per definition involved in real estate investment

activities, and there is typically a minimum number of investors . Furthermore a high pay-out ratio (80-90%) is typical for the REITs of the aforementioned countries. This high pay-out ratio severely limits the amount of operational cash available for non P&L related cash outflows (i.e. capital expenditures,

acquisitions and loan amortisation). As all European listed REITs are obliged to use IFRS and deprecation is therefore very limited, European REITs are

therefore highly dependent on either external financing or the sale of real estate investment properties for the generation of liquidity.

This high dependency on external funding is –when compared to other

industries- reflected a relatively high LTV ratio’s, which in accordance with the pecking order theory is the result of the absence of internal funds. However the use of third party debt for REITs is capped either through a direct limit on the leverage ratio or indirectly through an interest rate cover ratio.

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3. Data and Methodology

3.1 Data

This study uses a sample containing European publically traded REITs. The analysis is restricted to the following countries: the Netherlands (6 REITs), Belgium (12 REITs), and France (26 REITs). These countries are the only

European countries to have REIT legislation in place for the whole sample period (2004-2014). For the aforementioned sample period (2004-2014) data is

derived from Bloomberg. From Bloomberg both daily total stock returns of each individual REIT are derived as well as balance sheet data. The balance sheet data unfortunately is not available on a monthly basis and is therefore collected as per year end. The 3-month EURIBOR (also derived from Bloomberg) is used as the risk-free rate in order to calculate excess returns. The Fama-French (1993) market return (Rm), size (SMB), book-to-market (HML) and momentum (MOM) factors are from Ken French’s website.

As mentioned previously, data has been collected for the period from January 2004 to December 2014. The first three years are prior to the crisis and for the purposes of this analysis are defined as period one. Period two –the crisis- commences in March 2007 and lasts till the beginning of March 2009. This is the shaded area in the Figure 1 below. The EPRA/NAREIT Developed Europe index -composed of European listed real estate companies- drops dramatically during this period. The third period –commencing the beginning of March 2009- is the post crisis period. As can be seen in figure one the real estate related crisis commences somewhat later than the general stock market crisis. Moreover prior to the crisis real estate related shares appreciated more than the general stock market and lost more of their value during the crisis. As such one would expect Betas with respect to the market which are higher than one. This however is not the case. Betas for the sample are found to be substantially lower than one. These low REIT beta’s are in accordance with other studies. Packer et al. (2014) for instance shows that for the pre-crises period beta’s varying form 0.14-0.34 are the norm for Dutch, Belgian and French REITs. During and after the crisis

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according to the aforementioned study beta’s went up but still substantially lower than one (i.e. 0.34-0.77). These higher beta’s are said to be the result of the growth of the REIT sector and general integration with the stock market, which then results in more efficient pricing. As is shown in the section “results” these higher Betas are not found in the pre sent study.

Figure 1 FTSE Eurotop 100 Index and the EPRA/NAREIT Developed Europe Index for the period January 2004 to December 2014

In order to examine the significance of idiosyncratic risk, Figure 2 - following Ooi et al (2009) - shows the proportion of idiosyncratic risk as a proportion of total return volatility. Specifically the percentage of idiosyncratic volatility –calculated on a monthly basis by regressing the daily stock returns on the Fama-French (1993) three factor model (as described in the next section)-is calculated as the proportion of the variance due to idiosyncratic risk as 𝜎𝜀2/ 𝜎𝑅𝐸𝐼𝑇2 . As can been

seen in Figure 2 the proportion of the sample variance unexplained by the Fama-French (1993) three factor model is very dominant over the whole period. Between 2004 and 2014 some 74.9% of the total variance is unexplained by the aforementioned Fama-French three factor model, and as such accounts for most of the total variance.

0% 50% 100% 150% 200% 250% 300% 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 FTSE Europetop 100 Index EPRA/NAREIT Developed Europe Index

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Figure 2 Idiosyncratic risk as a proportion of total volatility for Dutch, Belgian and French stocks for the period January 2004 to December 2014.

This is consistent with the findings of Ooi et al. (2009) who find an average of 78.3% idiosyncratic risk versus total variance for the US REIT market for the period 1990 to 2005. As can be seen from the trend line in Figure 2 the

proportion of idiosyncratic volatility versus total volatility is showing a lightly downwards trend. This downwards trend is not surprising given the growth of the REIT sector over recent years, and the further integration into the general stock market. This further integration into the general stock market has also resulted in higher Betas according to the aforementioned Packer et al. (2014). This may have resulted in a more efficient pricing of REITs.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 % Idiosyncratic risk over total risk

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3.2 Methodology

Past idiosyncratic risk research on REITs has either focused on measuring idiosyncratic volatility at portfolio level (inter alia Chiang et al (2009), Ang et al (2006), DeLisle (2013)) or at the level of individual firms (inter alia Sun &Yung (2009), Ooi et al (2009)). This thesis focuses on the firm level analysis with a special attention on the impact of the use of third party debt on the

(idiosyncratic) risk return-relationship.

Measuring idiosyncratic volatility

The idiosyncratic risk of each REIT is calculated using three methods. First, following Sun and Yung (2009) the monthly idiosyncratic volatility is calculated using the CAPM calculation method. The following regression is run for each REIT:

𝑅_𝑡𝑖 _{− 𝑟}

𝑓,𝑡 = 𝛼𝑡𝑖 + 𝛽𝑚𝑘,𝑡𝑖 (𝑅𝑚𝑘,𝑡− 𝑅𝑓,𝑡) + 𝜀𝑡𝑖 (3)

where 𝑅_𝑡𝑖 _{− 𝑟}

𝑓,𝑡 is the excess return for REIT i at time t, α is the intercept,

𝛽_{𝑚𝑘,𝑡}𝑖 (𝑅𝑚𝑘,𝑡 − 𝑅𝑓,𝑡) is measured as the sample covariance between the monthly

REIT returns and the monthly excess REIT market-portfolio returns , and 𝜀_𝑡𝑖_is

the error term.

Secondly, the monthly idiosyncratic volatility is also calculated using Fama-French three-factor model (1993). The following regression is run for each REIT: 𝑅_𝑡𝑖 _{− 𝑟}

𝑓,𝑡 = 𝛼𝑡𝑖 + 𝛽𝑚𝑘,𝑡𝑖 (𝑅𝑚𝑘,𝑡− 𝑅𝑓,𝑡) + 𝛽𝑆𝑀𝐵,𝑡𝑖 𝑆𝑀𝐵𝑡+ 𝛽𝐻𝑀𝐿,𝑡𝑖 𝐻𝑀𝐿𝑡+ 𝜀𝑡𝑖 (4)

𝑓,𝑡, α, (𝑅𝑚𝑘,𝑡− 𝑅𝑓,𝑡) and 𝜀𝑡𝑖 have been discussed previously. 𝑆𝑀𝐵𝑡𝑖 is

the small cap effect , 𝐻𝑀𝐿_𝑡 is the value effect,. Both the 𝑆𝑀𝐵_𝑡𝑖_{and the}

𝐻𝑀𝐿𝑡factors are derived from Kenneth French’s website. Thirdly the monthly

idiosyncratic risk is also calculated according to the Carhart (1997) method now also incorporating momentum effects:

𝑅_𝑡𝑖 _{− 𝑟} 𝑓,𝑡 =

𝛼_𝑡𝑖_{+ 𝛽}

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𝑓,𝑡, α, (𝑅𝑚𝑘,𝑡− 𝑅𝑓,𝑡) 𝑆𝑀𝐵𝑡𝑖, 𝐻𝑀𝐿𝑡 and 𝜀𝑡𝑖 have been discussed

previously, and 𝑀𝑂𝑀_𝑡𝑖_{is the momentum factor.}

Next the idiosyncratic risk IDIO of each REIT i is calculated –for both the CAPM, the Fama-French three factor and the Carhart four-factor calculation method- as the standard deviation of the error term:

𝐼𝐷𝐼𝑂_𝑡𝑖 _{= (}1 𝑁∑ (𝜀𝑡 𝑖 _{− 𝜀} 𝑎𝑣𝑒𝑟𝑎𝑔𝑒,𝑡𝑖 )2 𝑁 𝑡=1 ) 1/2 (6)

where N is the number of days in that month and 𝜀_𝑖,𝑡2 are the squared residuals from the error term minus the average residual for that month . This calculation method avoids the introduction of a look-ahead bias when modelling

idiosyncratic volatility through EGARCH models (Fink et al. 2012, Guo et al. 2013).

Multivariate regressions

DeLisle et al (2013) emphasis the need for a regression based analysis when dealing with relative small samples, as is the case with the current thesis. This is done by applying the Fama-French cross sectional regression approach

controlling for a number of variables. In the manner also performed by inter alia Sun & Yung (2009) and DeLisle et al. (2013). This approach allows for the

simultaneous control of multiple factors. Then we test whether the coefficient on the lagged idiosyncratic volatility is significantly different from zero. Newey West (1987) standard errors are used to control for autocorrelation. The cross-sectional regression takes the following form:

𝑅_𝑡𝑖 _{− 𝑟} 𝑓,𝑡 = 𝛼𝑡𝑖 + 𝛾𝑆𝑀𝐵,𝑡𝑖 𝐼𝐷𝐼𝑂𝑡−1𝑖 + 𝛾𝐷𝐸,𝑡𝑖 𝐷𝐸𝑡𝑖+ 𝛾𝐷𝐸2,𝑡𝑖 𝐷𝐸2𝑡𝑖 + 𝛾𝑚𝑘,𝑡𝑖 (𝑅𝑚𝑘,𝑡− 𝑅𝑓,𝑡) + 𝛾_{𝑆𝑀𝐵,𝑡}𝑖 _𝑆𝑀𝐵 𝑡+ 𝛾𝐻𝑀𝐿,𝑡𝑖 𝐻𝑀𝐿𝑡+ 𝛾𝑀𝑂𝑀,𝑡𝑖 𝑀𝑂𝑀𝑡+𝜀𝑡𝑖 (7) Where 𝑅_𝑡𝑖_{− 𝑟}

𝑓,𝑡 is the excess return for REIT i during the month after time t, 𝑎𝑡 is

the intercept, , 𝐼𝐷𝐼𝑂_𝑡𝑖_{𝑖𝑠 𝑡ℎ𝑒 idiosyncratic risk of REIT i of the month previous to t,}

𝐷𝐸_𝑡𝑖_{is the leverage of REIT i (t=-1), 𝐷𝐸2} 𝑡

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(t=-1) to account for any potential non-linear relationship, 𝛽_{𝑚𝑘,𝑡}𝑖 _(𝑅

𝑚𝑘,𝑡− 𝑅𝑓,𝑡) is

systematic risk of the REIT market, 𝑆𝑀𝐵_𝑡𝑖_{is the small cap effect , 𝐻𝑀𝐿}

𝑡 is the

value effect, 𝑀𝑂𝑀_𝑡𝑖_{is the momentum effect, and finally 𝜀}

𝑡𝑖 is the error term and is

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4. Results

4.1 Descriptive statistics over idiosyncratic risk categories

Table 1 shows the descriptive statistics for the three sub-periods which illustrate the very different market environments for each period. For each period the sample is split into three sub-samples according to their idiosyncratic risk category –low, medium or high. As described in the previous section, idiosyncratic risk is calculated according to three different methods: CAPM, Fama-French three factor model (1993) and the Carhart (1997) four factor model. Idiosyncratic risk categorisation is done by ordering all REITs from lowest to highest idiosyncratic risk prior to the beginning of each month. The portfolio is then split into three equal parts i.e. low medium and high

idiosyncratic risk. This tabulation over different idiosyncratic allows comparison of the different characteristics of the sample for each sub-period.

With respect to the height of the idiosyncratic risk, table 1 shows that across all three risk categories idiosyncratic risk is substantially higher during than before and after the crisis. The periods before and after the crisis are comparable with respect to the height of the calculated idiosyncratic risk, and are comparable to the pre-crisis values found by DeLisle et al. (2013).

With respect to the “one month ahead excess return” of the REITs it can be seen that for the pre- and post-crises periods, as idiosyncratic risk increases the “one month ahead excess return” also increases. The positive sign is in accordance with what both Sun & Yung (2009), Ooi et al (2009) found for the US market, and contrary to the findings of DeLisle et al (2013) who use a different method to calculate market risk. This finding is in accordance with Merton (1987), where investors expect higher returns in return for higher idiosyncratic risk. The difference in “one month ahead excess return” between the high and low idiosyncratic risk buckets is significant at a 95% confidence level except for the CAPM calculation method in the pre-crisis period where the difference is not

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significant. During the crisis-period a higher idiosyncratic risk is associated with a lower “one month ahead excess return”, a result which is not unexpected.

Table 1 Summary statistics for three methods of idiosyncratic risk calculation. * p<0.05, ** p<0.01, ***p<0.001

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The Sun & Yung (2009), Ooi et al. (2009) and studies are both performed on a pre-crises time period so comparison with these studies is not possible for the crisis. DeLisle et al. (2013) -whose sample period include the crisis - also find negative pricing with respect to idiosyncratic risk. The negative difference between high and low idiosyncratic risk is significant at a 90% confidence level for the Fama-French three factor model and the Carhart four-factor model. From table 1 it also becomes clear that -for the pre-crisis and crisis period- as idiosyncratic risk increases Debt to Equity (DE) also increases. The difference in DE between the high idiosyncratic bucket and the low idiosyncratic bucket is significant at a 95% level except for the crisis CAPM calculation method.

According to theory the effects of leverage should impact beta i.e. systematic risk (and through beta also returns) rather than idiosyncratic risk. However for the downturn one can expect the (non-linear) effects of potential financial distress (such as bankruptcy costs, i.e. auditors fees, legal fees, reduced management attention to operations etc. plus the higher interest margins when financial distress occurs) to become more important, and these non-linear costs could be related to higher idiosyncratic risk. For the third post-crisis period the

relationship between idiosyncratic risk and DE is less clear cut. For this period all three calculation methods show a slight decrease in DE as idiosyncratic risk increases. However the difference between high and low is not significant at a 95% level. This is in accordance with financial theory, where the effects of leverage are through beta rather than directly. Giacomini et al (2014) also find a significant positive relationship between leverage and REIT returns before and after the crisis, and a significant negative relationship during the crisis. Their study does not however take idiosyncratic risk into account, so the question is whether this significant positive relationship would remain after correcting for idiosyncratic risk.

With respect to betas the picture is less clear cut than for the other variables. One does not expect a relationship between beta and idiosyncratic risk so this is in accordance with financial theory. What is remarkable, is that the betas are relatively low i.e. far below one. As described in the section “data” this is

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accordance with the study performed by Packer et al. (2014) The present study does not show a general increase in betas as shown by Packer et al (2014). From table 1 it can also be seen that the relationship between idiosyncratic risk and the size of the REIT, measured as balance sheet total or market capitalisation is not quite clear cut. Only after the crisis are high idiosyncratic risk companies significantly smaller in size. Sun and Yung (2009) also find that high

idiosyncratic risk is associated with smaller companies. They say that this could be the result of information inefficiencies. For the current data set, the

difference between low and high idiosyncratic risk the is not significant before and during the crisis. This is consistent with Chaudry et al. (2004) who also find that there is no significant relationship between company size and idiosyncratic risk.

4.2 Regression analysis

Figure 3, 4 and 5 show the results from the regression analysis for the Fama-French three factor idiosyncratic risk, for the pre-crisis period one, the crisis period two and the post-crisis period three. The results of the CAPM and Carhart four-factor model paint a similar picture and can be found in the Appendix. Model 1 simply regresses the excess REIT returns with respect to the excess market returns (RmRf). In contrast to Sun & Yung (2009) and DeLisle et al. (2013) all regression models for all periods show a significant positive relationship between returns and systematic risk.

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Figure 3 Regressions, period 1 (Pre-crisis)

Figure 4 Regressions, period 2 (Crisis)

* p<0.05, ** p<0.01, *** p<0.001 BIC -3032.8 -3029.8 -3022.2 -3035.8 -3031.4 dres 1096 1095 1093 1091 1090 R-sqr 0.037 0.040 0.046 0.070 0.072 (0.00) (0.00) (0.01) (0.01) (0.01) constant 0.012*** 0.007 0.012 0.010 0.010 (0.12) MOM -0.175 (0.09) (0.10) HML 0.448*** 0.387*** (0.09) (0.10) SMB 0.310*** 0.354*** (0.01) (0.01) (0.01) DE2 0.011 0.011 0.011 (0.02) (0.02) (0.02) DE -0.017 -0.018 -0.017 (0.08) (0.08) (0.08) (0.08) IDIO 0.106 0.094 0.093 0.093 (0.10) (0.10) (0.10) (0.10) (0.11) RmRf 0.564*** 0.576*** 0.575*** 0.506*** 0.591*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5 > r bic, fmt(3 0 1) label (R-sqr dres BIC))

* p<0.05, ** p<0.01, *** p<0.001 BIC -1701.2 -1716.8 -1706.6 -1719.4 -1713.2 dres 884 883 881 879 878 R-sqr 0.118 0.140 0.144 0.169 0.169 (0.00) (0.01) (0.01) (0.01) (0.01) constant -0.018*** 0.007 0.020 0.023* 0.023* (0.06) MOM -0.046 (0.17) (0.18) HML -0.025 -0.074 (0.09) (0.09) SMB 0.415*** 0.390*** (0.00) (0.00) (0.00) DE2 0.006 0.006 0.005 (0.01) (0.01) (0.01) DE -0.023* -0.024* -0.024* (0.13) (0.13) (0.13) (0.13) IDIO -0.339** -0.325* -0.258* -0.267* (0.07) (0.07) (0.07) (0.08) (0.08) RmRf 0.651*** 0.575*** 0.577*** 0.575*** 0.580*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5

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Figure 5 Regressions, period 3 (Post-crisis)

Model 2 adds idiosyncratic risk (IDIO) to the regression equation. For the pre-crisis and post-pre-crisis periods the relationship between idiosyncratic risk and expected returns is positive. This positive relationship is significant at a 90% confidence level for the post-crises period but not significant for the pre crises period. As mentioned in the previous section this positive relationship is in accordance with both Sun & Yung (2009), Ooi et al (2007). For the crisis period the sign of the relationship between idiosyncratic risk and expected returns is negative. For the Model 2 crisis-period this result is significant at a 95% confidence level. After adding control variables this significance is reduced to 90% confidence level. For the crisis period one can also see that without

idiosyncratic risk the systematic risk pricing is too high (i.e. Model 1 versus the other models).

As mentioned previously DeLisle et al. (2013) also finds a negative pricing for idiosyncratic risk. The relationship between idiosyncratic risk and expected returns is in concordance with the findings in the previous section for all three periods.

The effects of adding leverage (either simple – DE- or quadratic – DE2-) to the equation are modelled in Model 3. The effect is insignificant for both the pre- (negative) and the post crises (positive) period. This is in complete accordance

* p<0.05, ** p<0.01, *** p<0.001 BIC -5478.0 -5519.3 -5504.3 -5531.0 -5527.0 dres 2019 2018 2016 2014 2013 R-sqr 0.160 0.180 0.180 0.197 0.198 (0.00) (0.01) (0.01) (0.01) (0.01) constant 0.005*** -0.011 -0.013 -0.012 -0.014 (0.04) MOM 0.070 (0.07) (0.08) HML 0.111 0.155* (0.06) (0.06) SMB 0.240*** 0.283*** (0.00) (0.00) (0.00) DE2 -0.000 -0.000 -0.000 (0.01) (0.01) (0.01) DE 0.003 0.002 0.002 (0.14) (0.14) (0.14) (0.14) IDIO 0.294* 0.294* 0.278* 0.295* (0.05) (0.04) (0.04) (0.05) (0.05) RmRf 0.694*** 0.693*** 0.693*** 0.631*** 0.633*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5

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with financial theory where leverage should not be a pricing factor per se but should affect the pricing through the amplification effects on beta.

For the crisis period the effect of adding debt as a control factor is significant (at a 90% confidence level) and negative, while the square D/E term is never

significant. In as much that according to financial theory leverage should not be priced directly, the negative sign is exactly how one would expect it to be: it exacerbates the negative effects of the downturn. Given the tight credit market during the crisis where the costs of refinancing were higher than before it is not surprising that more leverage is perceived as negative. The adding of leverage as a factor does not seem to affect the pricing of idiosyncratic risk. As such the hypothesis as described in section one, i.e. that leverage affects pricing through idiosyncratic risk is not found in the cross sectional results. Giacomini et al (2014) find a significant positive relationship between leverage and REIT

returns before and after the crisis, and a significant negative relationship during the crisis. As mentioned previously they do not -however- not take idiosyncratic risk into the equation.

Model 4 adds the Fama-French small cap (SMB) and value effect (HML) to the equation. These do not significantly alter the effect of the excess market return or idiosyncratic risk effect except for the downturn period where the

idiosyncratic risk effect is smaller (less negative) when the small cap and value effect are added. Contrary to Ooi et al (2007) this study finds that the size and book-to market equity ratio factors are significant in the presence of

idiosyncratic risk. The Ooi et al. (2007) study however is focused on US REITS up to 2005. Sun and Yung (2009) also find a significant relationship for the SMB factor be it that the sign is negative in their study. Giacomini (2014), without studying the effects of idiosyncratic risk find a significant positive relationship for the SMB factor and a significant relationship for the HML factor with a sign varying across different countries.

Model 5 adds the Carhart momentum factor (MOM) to the regression. The results for the idiosyncratic risk factor are not significantly different from Model 4. As such this variable does not seem to affect the results significantly. This

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finding is contrary to Ooi et al. (2007) where the significant explanatory power of the momentum factor is robust in the presence of idiosyncratic risk. As mentioned before that study however is focused on US REITS up to 2005. Sun and Yung (2009) also find a significant negative relationship for the MOM factor, but their sample covers the same REITs as the Ooi et al. (2007) study. Giacomini (2014) does find a significant positive relationship for the momentum factor for Belgium but not for France or the Netherlands.

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5. Conclusion

This thesis has shown that –contrary to the CAPM theory- significant negative relationship is found between idiosyncratic risk and returns for Belgian, Dutch and French listed REITs during the crisis, and that this relationship is

significantly positive for the post-crises period. This finding suggests that idiosyncratic risk does indeed matter for REIT pricing. The finding that idiosyncratic risk is priced is in concordance with research done by Ooi et al (2009), Sun and Yung (2009) and DeLisle et al (2013) on US REITs. For the pre-crisis period there is also a positive relationship between idiosyncratic risk and pricing but this result is not significant at a 90% level.

This thesis also studies the role third party debt plays in the idiosyncratic risk-return relationship. During the crisis there is a significant negative relationship between leverage and returns but even though leverage seems to be associated with higher idiosyncratic risk it does not seem to play a significant role in the idiosyncratic risk return relationship. The finding that leverage is priced in the downturn is also found by Giacomini et al. (2014) in their study on the

relationship between leverage and returns. Before and after the crisis the inclusion of leverage into the idiosyncratic-risk return relationship does not seem to have any significant impact.

Areas for further research include expanding the European data set to non-REITs to test both for the pricing of idiosyncratic risk and the impact of leverage, and investigating whether the inclusion of leverage has any impact on the pricing of idiosyncratic risk in the US. Moreover further research areas could include the further analysis on the non-linear impact of the costs of financial distress.

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References

Abugri BA, Dutta S., (2014). Are we overestimating REIT idiosyncratic risks? Analysis of pricing effects and persistence. International Review of Economics

&Finance, Vol 29 249-259

Ang A., Hodrick, R.J., Xing, Y., Zhang, X. (2006) The cross section of volatility and expected returns. The Journal of Finance, 61, 259-299

Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). The cross‐section of volatility and expected returns. The Journal of Finance, 61(1), 259-299

Baum, A., and Farrelly, K. (2009). Sources of alpha and beta in property funds.

Journal of European Real Estate Research, 2/3, 218-234.

Blundell G.F., Fairchild S., Goodchild R. N. (2005). Managing Portfolio Risk in Real Estate. Journal of Property Research, Volume 22, Issue 2 & 3 , pages 115 – 136

Brealey, R.A. and S.C. Myers (2003). Principles of Corporate Finance, 7th ed., McGraw-Hill, NewYork, NY.

Brown, G. R., & Matysiak, G. A. (2000). Real estate investment: A capital market

approach. Financial Times Prentice Hall.

Byrne P.J., Lee S., (2001). Risk Reduction and Real Estate Portfolio Size.

Managerial and Decision Economics, Vol. 22, No. 7, pp. 369-379

Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of

finance, 52(1), 57-82.

Callender, M., Devaney, S., Sheahan, A., & Key, T. (2007). Risk reduction and diversification in UK commercial property portfolios. Journal of Property

Research, 24(4), 355-375.

Chaudhry, M.K., Maheshwari, S., & Webb, J.R. (2004), REITs and idiosyncratic risk. Journal of Real Estate Research, 26, 207–222.

DeLisle, R. J., Price, S. M., & Sirmans, C. F. (2013). Pricing of volatility risk in REITs. Journal of Real Estate Research, 35(2), 223-248

Fabozzi, F.J., (2000) Fixed Income Analysis for Chartered Financial Analysts Program, Frank J Fabozzi Associates, Pennsylvania, NY.

(36)

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.

Faulkender, M., & Petersen, M. A. (2006). Does the source of capital affect capital structure? Review of financial studies, 19(1), 45-79.

Feng, Z., Ghosh, C. and Sirmans, C. (2007) On the Capital Structure of Real Estate Investment Trusts (REITs). The Journal of Real Estate Finance and Economics, vol. 34(1): 81-105.

Fink, J.D., Fink K.E., He, H. (2012) Expected Idiosyncratic Volatility Measures and Expected Return. Financial Management 41:3, 719-67

Fu, F. (2009). Idiosyncratic risk and the cross-section of expected stock returns.

Journal of Financial Economics, 91(1), 24-37

Fuerst, F., & Matysiak, G. (2013). Analysing the performance of nonlisted real estate funds: a panel data analysis. Applied Economics, 45(14), 1777-1788.

Geltner, David. 2006. Commercial Real Estate Analysis and Investments,

International Edition, 2007-1011

Giacomini, E., Ling, C.L. & Naranjo, A., (2014). Leverage and returns: a cross-Country Analysis of Public Real Estate Markets, Journal of Real Estate Finance

and Economics, 2014-11-16

Giambona E., Harding J.P., Sirmans C.F., (2008). Explaining variation in REIT capital structure: The Role of Asset Liquidation Value. Real Estate Economics, Volume 36, Issue1 pp. 111-137

Graff R.A., and Michael S. Young (1996). Real estate return correlations: Real-world limitations on relationships inferred from NCREIF data. The Journal of Real

Estate Finance and Economics Volume 13, Number 2

Grovenstein, R., Harding, J, Sirmans, C.F, Thebpanya, S, and Turnbull, G. (2005) Commercial mortgage underwriting: How well do lenders manage risk? Journal

of Housing Economics, 355-383.

Goetzmann, W. N., & Kumar, A. (2008). Equity portfolio diversification*. Review

of Finance, 12(3), 433-463.

Gomes, J. F., & Schmid, L. (2010). Levered returns. The Journal of Finance, 65(2), 467-494.

(37)

Guo, H., Kassa, H., & Ferguson, M. F. (2014). On the relation between EGARCH idiosyncratic volatility and expected stock returns. Journal of Financial and

Quantitative Analysis, 49(01), 271-296

Hamada, Robert S. "The effect of the firm's capital structure on the systematic risk of common stocks." The Journal of Finance 27.2 (1972): 435-452.

Hull, John C. (2008). Options, Futures and Other Derivatives. Seventh edition Kaplan, S.N., Zingales, L. (1997) Do investment cash flow sensitivities provide useful measures of financing constraints? Quarterly Journal of Economics, (112(1), 169-215

Markowitz, H. “Portfolio Selection.” Journal of Finance 7: 77-91, March 1952. Merton, R.C., (1974). On the Pricing of Corporate Debt: the risk structure of interest rates. Journal of Finance, 29(2), pages 449-470

Modigliani, F. and M.H. Miller. (1958) The Cost of Capital, Corporation Finance, and the Theory of Investment. American Economic Review, 48:3, 261-97

Newbould, G.D. and Poon, P.S. (1993) The minimum number of stocks needed for diversification. Financial Practice and Education , 3, 85-87

Newey, W. K., & West, K. D. (1987). Hypothesis testing with efficient method of moments estimation. International Economic Review, 777-787.

Packer, F., Riddiough, T., & Shek, J. (2014). A Global Tour of Commercial Property and REIT Markets. International Real Estate Review, 17(2), 241-274.

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk*. The journal of finance, 19(3), 425-442.

Spek, M. R., & Hoorenman, C., (2011), Leverage: Please Use Responsibly. Journal

of Real Estate Portfolio Management, Vol. 17 No. 2, 2011

Sun, L., Titman, S. D., & Twite, G. J. (2014). REIT and Commercial Real Estate Returns: A Postmortem of the Financial Crisis. Real Estate Economics.

Sun, Q., & Yung, K. (2009). Idiosyncratic risk and expected returns of equity real estate investment trusts. Journal of Real Estate Portfolio Management, 15(1), 45-57.

Ooi, JTL, Wang J., Webb JR., (2009). Idiosyncratic risk and REIT returns. The

(38)

Young, M.S, S. L. Lee, S. P. Devaney (2006). Non-Normal Real Estate Return Distributions by Property Type in the UK Journal of Property Research, Volume 23, Issue 2 pp 109 – 133

Westgaard, S., Eidet, A., Frydenberg, S., & Grosås, T. C. (2008). Investigating the capital structure of UK real estate companies. Journal of Property Research, 25(1), 61-87.

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APPENDIX 1: regression results for the CAPM and Carhart

four-factor idiosyncratic risk calculation methods

Figure 4 CAPM, period 1

. * p<0.05, ** p<0.01, *** p<0.001 BIC -2174.8 -2173.8 -2167.1 -2177.2 -2186.4 dres 804 803 801 799 798 R-sqr 0.057 0.064 0.072 0.098 0.116 (0.00) (0.00) (0.01) (0.01) (0.01) constant 0.011*** 0.002 0.010 0.010 0.013 (0.14) MOM -0.588*** (0.11) (0.13) HML 0.520*** 0.292* (0.10) (0.11) SMB 0.229* 0.331** (0.01) (0.01) (0.01) DE2 0.016 0.016 0.015 (0.02) (0.02) (0.02) DE -0.028 -0.027 -0.027 (0.09) (0.09) (0.08) (0.08) IDIO 0.142 0.134 0.116 0.108 (0.11) (0.11) (0.11) (0.11) (0.13) RmRf 0.688*** 0.716*** 0.716*** 0.689*** 0.997*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5 * p<0.05, ** p<0.01, *** p<0.001 BIC -1701.2 -1716.1 -1706.1 -1718.3 -1712.0 dres 884 883 881 879 878 R-sqr 0.118 0.140 0.143 0.168 0.168 (0.00) (0.01) (0.01) (0.01) (0.01) constant -0.018*** 0.006 0.019* 0.022* 0.022* (0.06) MOM -0.043 (0.17) (0.18) HML -0.033 -0.079 (0.09) (0.09) SMB 0.411*** 0.388*** (0.00) (0.00) (0.00) DE2 0.006 0.006 0.006 (0.01) (0.01) (0.01) DE -0.023* -0.025* -0.025* (0.10) (0.10) (0.10) (0.10) IDIO -0.284** -0.273** -0.211* -0.218* (0.07) (0.07) (0.07) (0.08) (0.08) RmRf 0.651*** 0.566*** 0.568*** 0.572*** 0.576*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5

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Figure 9: Carhart four-factor model, period 1

* p<0.05, ** p<0.01, *** p<0.001 BIC -5478.0 -5502.3 -5487.3 -5516.7 -5512.4 dres 2019 2018 2016 2014 2013 R-sqr 0.160 0.173 0.173 0.191 0.192 (0.00) (0.01) (0.01) (0.01) (0.01) constant 0.005*** -0.008 -0.010 -0.010 -0.012 (0.05) MOM 0.067 (0.07) (0.08) HML 0.116 0.158* (0.06) (0.06) SMB 0.248*** 0.290*** (0.00) (0.00) (0.00) DE2 -0.000 -0.000 -0.000 (0.01) (0.01) (0.01) DE 0.002 0.002 0.002 (0.13) (0.13) (0.13) (0.13) IDIO 0.214 0.214 0.206 0.223 (0.05) (0.04) (0.04) (0.05) (0.05) RmRf 0.694*** 0.705*** 0.705*** 0.640*** 0.643*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5 * p<0.05, ** p<0.01, *** p<0.001 BIC -3032.8 -3029.0 -3021.4 -3035.2 -3030.7 dres 1096 1095 1093 1091 1090 R-sqr 0.037 0.040 0.045 0.069 0.071 (0.00) (0.00) (0.01) (0.01) (0.01) constant 0.012*** 0.007 0.012 0.011 0.011 (0.12) MOM -0.174 (0.09) (0.10) HML 0.448*** 0.388*** (0.09) (0.10) SMB 0.311*** 0.355*** (0.01) (0.01) (0.01) DE2 0.011 0.011 0.011 (0.02) (0.02) (0.02) DE -0.017 -0.018 -0.017 (0.09) (0.09) (0.09) (0.09) IDIO 0.101 0.087 0.087 0.086 (0.10) (0.10) (0.10) (0.10) (0.11) RmRf 0.564*** 0.575*** 0.574*** 0.505*** 0.589*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5

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Figure 7 Carhart four-factor model, period 2

Figure 8 Carhart four-factor model, period 3

* p<0.05, ** p<0.01, *** p<0.001 BIC -1701.2 -1717.0 -1706.8 -1719.6 -1713.4 dres 884 883 881 879 878 R-sqr 0.118 0.141 0.144 0.169 0.169 (0.00) (0.01) (0.01) (0.01) (0.01) constant -0.018*** 0.007 0.020* 0.023* 0.024* (0.06) MOM -0.045 (0.17) (0.18) HML -0.027 -0.075 (0.09) (0.09) SMB 0.415*** 0.391*** (0.00) (0.00) (0.00) DE2 0.006 0.006 0.006 (0.01) (0.01) (0.01) DE -0.023* -0.024* -0.024* (0.13) (0.13) (0.13) (0.13) IDIO -0.347** -0.333* -0.266* -0.274* (0.07) (0.07) (0.07) (0.08) (0.08) RmRf 0.651*** 0.570*** 0.572*** 0.571*** 0.576*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5 > r bic, fmt(3 0 1) label (R-sqr dres BIC))

* p<0.05, ** p<0.01, *** p<0.001 BIC -5478.0 -5519.2 -5504.2 -5531.3 -5527.2 dres 2019 2018 2016 2014 2013 R-sqr 0.160 0.180 0.180 0.197 0.198 (0.00) (0.01) (0.01) (0.01) (0.01) constant 0.005*** -0.011 -0.013 -0.012 -0.014 (0.04) MOM 0.070 (0.07) (0.08) HML 0.112 0.156* (0.06) (0.06) SMB 0.241*** 0.284*** (0.00) (0.00) (0.00) DE2 -0.000 -0.000 -0.000 (0.01) (0.01) (0.01) DE 0.002 0.002 0.002 (0.14) (0.14) (0.14) (0.14) IDIO 0.295* 0.296* 0.281* 0.298* (0.05) (0.04) (0.04) (0.05) (0.05) RmRf 0.694*** 0.694*** 0.694*** 0.631*** 0.633*** b/se b/se b/se b/se b/se Model 1 Model 2 Model 3 Model 4 Model 5

Does the use of leverage impact the idiosyncratic risk-return relationship of listed REITs in the Netherlands, Belgium and France?

University of Amsterdam, Amsterdam Business School

Master in Real Estate Finance